Application of envelope theorem to determine the shapes of contact components in toroidal continuously variable transmission

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The efficiency of toroidal continuously variable transmission (CVT) is limited by the spin loss caused by different speed distributions of the contact areas between discs and rollers. Although two types of zero-spin CVTs are offered, a demerit in the form of difficult speed ratio variation is observed simultaneously. The core idea of this study is the realisation of a method based on the envelope theorem to optimise the shapes of discs and rollers. After the envelopes are calculated, two zero-spin CVTs (i.e. inner cone and outer cone CVTs) are proposed. The calculation of the spin ratio shows that the two proposed CVTs can both transmit power without the spin motion. The total efficiency of the proposed CVTs can therefore be improved, as evidenced by a widely accepted computational model. A comparison of the proposed CVTs and the conventional CVTs is conducted, and the results show that the durability properties of the proposed CVTs are both improved. Although it is hard to manufacture, the inner cone CVT surpassed the demerit of the control difficulty which remains observable in conventional zero-spin CVTs and the outer cone CVT.